Scales which are "maximally even" divisions of some equal-tempered universe have
several musically interesting properties. When a maximally even scale has a number
of notes (card
) that is coprime to the size of the equal-tempered universe, the
maximally even scale is called a "non-degenerate well-formed" or "moment of symmetry"
scale. When its size divides the equal temperament, it is a perfectly even scale. When
it is neither coprime nor a divisor, it produces a scale with a structure like the
octatonic (i.e. a union of perfectly even scales, or a well-formed scale with a period
smaller than the octave). The scale is generated by quantizing a perfectly even scale
to the chosen chromatic cardinality. Two quantization options are offered (rounding down
and rounding to the nearest value).